It greatly depends on what you mean as 'noticeable' - what/why do you want to synchronise, and how it reaches the ears from physical speakers.
Keep in mind that a sound source being 30cm/1 feet further from the ear is about the same effect as a millisecond of delay (speed of sound ~340m/s) - thus, synchronising on the order of microseconds is generally unneccessary unless you somehow have and need sub-millimeter localisation accuracy. That being said, small delays can cause phase cancellation issues which would be noticeable, but would depend on exact placement of sound sources.
However, if we're talking about the limits of the mind - there are two well known phenomena; first is the limit where mind perceives sound as simultaneous with visual stimulus (despite them really being slightly offset), and the second is where mind perceives two close-but-separate sound spikes as a single event (with the loudest masking the weaker). I can't find the exact limits now, but both of them should be somewhere between 1 millisecond and 5 milliseconds if I recall correctly.